On the bipartition numbers of random trees. II (Q2761041)
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scientific article; zbMATH DE number 1682903
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the bipartition numbers of random trees. II |
scientific article; zbMATH DE number 1682903 |
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17 December 2001
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bipartition number
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random tree
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0.88931805
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0.8750153
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0.87463534
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0.86966217
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On the bipartition numbers of random trees. II (English)
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[For Part I see \textit{J. W. Moon}, Ars Comb. 25C, 3-10 (1988; Zbl 0662.05018).]NEWLINENEWLINENEWLINEFor a rooted tree \(T_n\) with \(n\) vertices, let \(p=p(T_n)\) and \(q=q(T_n)\) denote the number of vertices at even and odd distances from the root, respectively. Let \(D(T_n)=|p-q |\). Thus, \(D(T_n)\) is the difference between the sizes of the two color classes in a proper \(2\)-coloring of \(T_n\). The authors investigate the limiting distribution, expected value, and variance of the numbers \(D(T_n)\) when the trees \(T_n\) belong to certain simply generated families of random trees.
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